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This paper proposes a generalization of the recently introduced successive cancellation flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard SC decoding. To make such an approach effective, we first introduce the concept of higher order bit flips and propose a new metric to determine the bit flips that are more likely to correct the trajectory of the SC decoding. We then propose a generalized SCFlip decoding algorithm, referred to as dynamic-SCFlip (D-SCFlip), which dynamically builds a list of candidate bit flips, while guaranteeing that the next attempt has the highest probability of success among the remaining ones. Simulation results show that D-SCFlip is an effective alternative to SC-list decoding of polar codes, by providing very good error correcting performance, with an average computation complexity close to the one of the SC decoder. [ABSTRACT FROM AUTHOR]

We consider the joint detection and decoding of m-sequences. The receiver has to decide whether an m-sequence is received and possibly to decode its initial state. To do so, it implements an iterative message-passing decoding algorithm that operates on a parity check matrix, built upon a number of reference parity-check equations satisfied by the m-sequence. This matrix concatenates several elementary parity check matrices which are derived from reference equations. Unlike the conventional decoding case, the detection problem imposes to consider false alarms that may occur when the decoder is only fed with noise. While absorbing sets are known to be responsible for the error floor phenomenon of iterative message-passing decoders, we show that they may have a beneficial effect on the detection performance, in that they may prevent the decoder to produce false alarms. We further compute the number of hybrid cycles of length six and eight in the Tanner graph of the decoder and use the minimization of this number as criterion to derive an algorithm for selecting the reference parity check equations. This algorithm was found to be efficient for minimizing the probability of false alarm and decreases also the probability of wrong detection in the very small SNR region. This has been achieved at the cost of a reduction of the probability of correct detection. [ABSTRACT FROM PUBLISHER]

This paper investigates the behavior of the Min-Sum decoder running on noisy devices. Our aim is to evaluate the robustness of the decoder to computation noise caused by the faulty logic in the processing units. This type of noise represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the finite-precision min-sum decoder and then carry out the density evolution analysis of the noisy min-sum decoder. We show that, in some particular cases, the noise introduced by the device can help the min-sum decoder to escape from fixed points attractors and may actually result in an increased correction capacity with respect to the noiseless decoder. We also point out a specific threshold phenomenon, referred to as functional threshold, which accurately describes the convergence behavior of noisy decoders. The behavior of the noisy MS is demonstrated in the asymptotic limit of the code length through a noisy version of density evolution and is also verified in the finite-length case by Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the problem of designing good non-binary LDPC codes for Slepian-Wolf coding. The design method is based on Density Evolution which gives the asymptotic error probability of the decoder for given code degree distributions. Density Evolution was originally introduced for channel coding under the assumption that the channel is symmetric. In Slepian-Wolf coding, the correlation channel is not necessarily symmetric and the source distribution has to be taken into account. In this paper, we express the non-binary Density Evolution recursion for Slepian-Wolf coding. From Density Evolution, we then perform code degree distribution optimization using an optimization algorithm called differential evolution. Both asymptotic performance evaluation and finite-length simulations show the gain at considering optimized degree distributions for SW coding. [ABSTRACT FROM AUTHOR]

Two error correction schemes are proposed for word-oriented binary memories that can be affected by erasures, i.e. errors with known location but unknown value. The erasures considered here are due to the drifting of the electrical parameter used to encode information outside the normal ranges associated to a logic 0 or a logic 1 value. For example, a dielectric breakdown in a magnetic memory cell may reduce its electrical resistance sensibly below the levels which correspond to logic 0 and logic 1 values stored in healthy memory cells. Such deviations can be sensed during memory read operations and the acquired information can be used to boost the correction capability of an error-correcting code (ECC). The proposed schemes enable the correction of double-bit errors based on the combination of erasure information with single-bit error correction and double-bit error detection (SEC-DED) codes or shortened (SEC) codes. The correction of single-bit errors is always guaranteed. Ways to increase the number of double-bit and triple-bit errors that can be detected by shortened SEC and SEC-DED codes are considered in order to augment the error correction capability of the proposed solutions. [ABSTRACT FROM AUTHOR]

We study the stability of the Picard bundle on the moduli space of stable vector bundles of fixed rank and determinant, over an irreducible, smooth, algebraic curve of genus g⩾2. To cite this article: V. Savin, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 885–888. [Copyright &y& Elsevier]

We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate randomly chosen from the Clifford group is used to combine two single-qubit channels. The inputs to the synthesized bad channels are frozen by preshared EPR pairs between the sender and the receiver, so our scheme is entanglement assisted. We further show that quantum polarization can be achieved by choosing the channel combining Clifford operator randomly, from a much smaller subset of only nine two-qubit Clifford gates. Subsequently, we show that a Pauli channel polarizes if and only if a specific classical channel over a four-symbol input set polarizes. We exploit this equivalence to prove fast polarization for Pauli channels, and to devise an efficient successive cancellation based decoding algorithm for such channels. Finally, we present a code construction based on chaining several quantum polar codes, which is shown to require a rate of preshared entanglement that vanishes asymptotically. [ABSTRACT FROM AUTHOR]

5G systems and networks are expected to provide unprecedented data-rate to final users and services, in combination with increased coverage and density. The traffic generated at the edges of the network should be hauled through high capacity data-conveyors. Extremely high data-rate links able to provide optical-fiber like performance in the order of 100 Gbps are required to reduce the cost and increase the flexibility of the network infrastructure deployment. This paper presents a full transceiver architecture based on a channel-bonding radio-frequency front-end operating at millimeter-wave frequencies and digital baseband processing units able to provide such data-rates with a feasible implementation in low-cost CMOS technologies. The baseband section of the receiver includes digital compensation algorithms that allow to cope with some of the radio front-end impairments. The main functionalities of the proposed transceiver architecture are validated in hardware. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an architecture-aware Progressive Edge Growth (PEG)-based construction method for Low-Density Parity-Check (LDPC) codes. We target optimization through code construction for layered architectures with pipelined processing and memory organized in single-port banks. For a given layered Quasy-Cyclic Low-Density Parity-Check (QC-LDPC) decoder architecture configuration, the code constraints need to maximize hardware usage efficiency. Implementation results for Field-Programmable Gate Array (FPGA) technology suggest that the codes obtained using the proposed algorithm have a throughput increase of 39% up to 110%, due to the increase in working frequency obtained by using pipeline. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing low-density parity check decoders robust to transient errors introduced by faulty hardware. We assume that the faulty hardware introduces errors during the message-passing updates, and we propose a general framework for the definition of the message update faulty functions. Within this framework, we define symmetry conditions for the faulty functions and derive two simple error models used in the analysis. With this analysis, we propose a new interpretation of the functional density evolution threshold introduced by Kameni et al. in the recent literature and show its limitations in the case of highly unreliable hardware. However, we show that under restricted decoder noise conditions, the functional threshold can be used to predict the convergence behavior of finite alphabet iterative decoders (FAIDs) under faulty hardware. In particular, we reveal the existence of robust and nonrobust FAIDs and propose a framework for the design of robust decoders. We finally illustrate robust- and nonrobust-decoder behaviors of finite-length codes using Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]